Question: Which of the following numbers is a multiple of 8? ${41,48,70,75,117}$
Answer: The multiples of $8$ are $8$ $16$ $24$ $32$ ..... In general, any number that leaves no remainder when divided by $8$ is considered a multiple of $8$ We can start by dividing each of our answer choices by $8$ $41 \div 8 = 5\text{ R }1$ $48 \div 8 = 6$ $70 \div 8 = 8\text{ R }6$ $75 \div 8 = 9\text{ R }3$ $117 \div 8 = 14\text{ R }5$ The only answer choice that leaves no remainder after the division is $48$ $ 6$ $8$ $48$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $8$ are contained within the prime factors of $48$ $48 = 2\times2\times2\times2\times3 8 = 2\times2\times2$ Therefore the only multiple of $8$ out of our choices is $48$. We can say that $48$ is divisible by $8$.